Yes, all three can be interchangeable if you are talking about a sentence like 'Go down the road'. You can say
'I went along the road'
'I went down the road'
'I went up the road'
and there is no practical difference between these sentences. If there is an obvious gradient to the road, 'up' or 'down' would be chosen, depending on whether you are climbing or descending the slope.
I happen to live part-way up a road which is very steep, so it would be very clear what I meant when I said 'I'm going up..' or 'going down..'. But you could also say 'go up' or 'go down' for roads that are completely flat, and this gives no indication of direction.
In many cases it's often just a personal choice - three different people might say the same thing in three different ways. 'I went up/down/along the road' often has nothing to do with whether the road is leading north or south, away or from the town, or any other real-world distinction. They're just alternative ways of expressing the same idea.